
By [1]}
(applying to general Borel spaces),
\(\mathbb {P}(\xi _S\in \cdot )\ll \mathbb {P}(\xi \in \cdot )\) . Hence
we also have \(\mathbb {P}(\xi _S\in \cdot )\ll \Pi _{\lambda _W}\) 
and we let \(g\colon {\mathbf {N}}\rightarrow {\mathbb {R}}_+\)  denote the corresponding density.
Then
\(I\le e^{\lambda (W)}\iint g(\psi _W)f(\psi _W+\mu _{W})\,\Pi _\lambda (\mathrm {d}\mu )\,\Pi _\lambda (\mathrm {d}\psi ).\) 
